Theorems · Theorem · order theory
Finset.sup_id_eq_sSup
∀ {α : Type u_2} [inst : CompleteLattice α] (s : Finset α), s.sup id = sSup ↑s- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement · cited by 8,199
- iSupproof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement · cited by 954
- Finset.supstatement · cited by 530
- iSup_congr_Propproof · cited by 247
- sSup_eq_iSupproof · cited by 42
- Finset.sup_eq_iSupproof · cited by 30
Cited by12
Results whose statement or proof uses this declaration.
- MeasureTheory.IsSetSemiring.exists_finpartition_sdiffproof · cited by 8
- MeasureTheory.IsSetSemiring.sdiff_sUnion_eq_sUnion_disjointOfDiffUnionproof · cited by 6
- Finset.sup_id_set_eq_sUnionproof · cited by 4
- inf_sSup_eq_iSup_inf_sup_finsetproof · cited by 4
- IsCompactlyGenerated.BooleanGenerators.atomisticproof · cited by 4
- MeasureTheory.IsSetSemiring.sUnion_disjointOfDiffproof · cited by 3
- WellFoundedGT.finite_of_sSupIndepproof · cited by 2
- CompleteLattice.WellFoundedGT.isSupFiniteCompactproof · cited by 2
- Submodule.fg_iff_compactproof · cited by 1
- sSupIndep_iff_finiteproof · cited by 1
- TopologicalSpace.NoetherianSpace.exists_finset_irreducibleproof · cited by 0
- Finset.sup_eq_sSup_imageproof · cited by 0